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A085308 Iterate function described in A085308 (= reverse concatenation of prime factors); a(n) is either 1# the fixed point[=prime] if it exists at all: 2# a(2k)=1 labels that no convergence with most even initial values, in contrary mostly rapid divergence is the case; 3# a(n)=0 if n=1 or if the iteration results in nontrivial attractor with cycle length larger than one. 4
0, 2, 3, 2, 5, 2, 7, 2, 3, 1, 11, 2, 13, 2, 53, 2, 17, 2, 19, 1, 73, 2, 23, 2, 5, 1, 3, 2, 29, 1, 31, 2, 113, 2, 53, 2, 37, 2, 197, 1, 41, 1, 43, 2, 53, 1, 47, 2, 7, 1, 173, 1, 53, 2, 41113, 2, 193, 1, 59, 1, 61, 1, 73, 2, 53, 1, 67, 1, 233, 1, 2, 73, 1, 53, 1, 197, 1, 79, 1, 3, 1, 83, 1, 53, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..85.

FORMULA

Algorithm:

1. factorize n;

2. arrange prime factors by decreasing size;

3. concatenate prime factors and interpret the result as a decimal number.

EXAMPLE

n=even: remains even: m = 100 = 2*2*5*5 -> {2,5} -> {5,2} -> 52 = a(100);

n = 2^i*3^j: a(n)=2 since iteration list is {n,32,2}; these

are the known convergent even cases of initial value.

n=143: a(143) = 44864859110711 because the iteration list is

{143, 1311, 23193, 8593, 66113, 388917, 547793, 2273241, 55311373, 989474313, 8914183373, 84859143973, 528059391607, 44864859110711};

a(n) = 0 for n = 213, 323, 639, 713 ending in {713, 3123, 3473, 15123}; terminal orbit of length = 4.

All possible cases occur: fixed point, divergence, terminal cycle.

MATHEMATICA

ffi[x_] := Flatten[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] lf[x_] := Length[FactorInteger[x]] nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] rec[x_] := Fold[nd, 0, Flatten[IntegerDigits[Reverse[ba[x]]], 1]] Table[rec[w], {w, 1, 128}]

CROSSREFS

Cf. A084317-A084319, A085308, A085309.

Sequence in context: A136096 A284694 A072591 * A209190 A086286 A272565

Adjacent sequences:  A085305 A085306 A085307 * A085309 A085310 A085311

KEYWORD

base,nonn

AUTHOR

Labos Elemer, Jun 27 2003

STATUS

approved

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Last modified June 17 22:17 EDT 2019. Contains 324200 sequences. (Running on oeis4.)